From physical to human capital accumulation: Effects of mortality changes

Review of Economic Dynamics 34 (2019) 103–120

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From physical to human capital accumulation: Effects of mortality changes Keiya Minamimura a,b , Daishin Yasui c,∗ a b c

Kansai Gaidai University, Japan Graduate School of Economics, Kobe University, Japan Kyoto University, Japan

a r t i c l e

i n f o

Article history: Received 10 May 2018 Received in revised form 12 March 2019 Available online 21 March 2019 JEL classification: I10 J10 O11 O40

a b s t r a c t This paper develops a growth model à la Galor and Moav (2004) that captures the replacement of physical capital accumulation by human capital accumulation as the prime engine of growth. We show that (i) decreased mortality promotes this replacement, and (ii) the effect of a decrease in mortality on per-capita income differs across the phases of the development process. A notable prediction of our theory is that the higher the level of education in an economy, the more likely it is that a decrease in mortality will increase income per capita. Using finite mixture models, we show that this prediction is supported by the data. Our results provide a new interpretation on the negative effect of life expectancy on growth reported by Acemoglu and Johnson (2007). © 2019 Elsevier Inc. All rights reserved.

Keywords: Growth Mortality Human capital Physical capital Overlapping generations model

1. Introduction Does a decrease in mortality raise income per capita? An influential paper by Acemoglu and Johnson (2007) provoked a controversy over this question. In contrast to studies based on cross-country variation (e.g., Lorentzen et al., 2008), Acemoglu and Johnson (2007) use instruments for mortality changes to solve the endogeneity problem, and obtain a surprising result: improved life expectancy has a positive effect on population growth, but a negative effect on GDP per capita. This result is somewhat surprising because it implies a trade-off between health improvement and economic growth. Theoretically, their result is justified by the dilution effect in traditional growth theories: population growth decreases land per capita (the Malthus channel) and physical capital per capita (the Solow channel), thus reducing income per capita. On the other hand, recent growth literature suggests the increasing importance of human capital over land and physical capital as an engine of growth, particularly in developed countries (e.g., Jones and Romer, 2010). Here, we develop a growth model in which the replacement of physical capital accumulation by human capital accumulation is endogenous, and mortality changes affect the replacement process. Furthermore, we investigate, theoretically and empirically, how a decrease in mortality affects income per capita.

*

Corresponding author. E-mail addresses: [email protected] (K. Minamimura), [email protected] (D. Yasui).

https://doi.org/10.1016/j.red.2019.03.005 1094-2025/© 2019 Elsevier Inc. All rights reserved.

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We extend the model of Galor and Moav (2004), which captures the replacement of physical capital accumulation by human capital accumulation as a prime engine of growth, in order to consider the effect of mortality changes on the development process. Our model derives two key results: (i) decreased mortality promotes this replacement; and (ii) the effect of a decrease in mortality on per-capita income differs across the phases of the development process. As in Galor and Moav (2004), we shed light on the portfolio choice between physical and human capital. However, our focus differs from theirs. We focus on an asymmetry between physical and human capital: human capital is inherently embodied in people and, thus, it yields a return only when the investor survives, whereas physical capital is disembodied and, thus, its returns belong to other people (e.g., a spouse, siblings, offspring), even if the investor dies. This asymmetry implies that in environments with high mortality, it may not be profitable for households to concentrate their assets in human capital. A decrease in mortality stimulates the incentive to invest in human capital, and promotes the replacement of physical capital accumulation with human capital accumulation.1 Many studies have established the theoretical result that a decrease in mortality promotes human capital investment, based on the Ben-Porath effect (e.g., De la Croix and Licandro, 1999; Kalemli-Ozcan et al., 2000; Boucekkine et al., 2002; 2003; Soares, 2005; Cervellati and Sunde, 2005). The conventional channel through which the Ben-Porath effect operates is as follows. Human capital continues to yield a return as long as agents are able-bodied workers once they form human capital, while physical capital investment yields a once-off return. Thus, a lower mortality prolongs the working life over which investments in human capital pay off, thereby positively affecting human capital investment.2 The novelty of this study is to shed light on the embodied nature of human capital, which depreciates fully with the death of the individual, and the disembodied nature of physical capital, which remains after death. Physical capital can be used to improve the living standards of surviving family members after the death of the original investor because it is left to them in the form of bequests. On the other hand, human capital cannot be used in such a way because it ends with deceased person. The embodied nature of human capital and the disembodied nature of physical capital result in physical capital having an advantage over human capital as intergenerationally-transferred resources. This advantage is large when mortality is high and, thus, a decline in mortality induces agents to substitute human capital for physical capital.3 In our model, an economy switches from a regime where only physical capital is accumulated to a regime where both physical and human capital are accumulated during the development process. In the former regime, a decrease in mortality depresses income per capita by the dilution effect on physical capital, especially in the short run. In the latter regime, however, two additional effects improve the average amount of human capital in the labor market. First, a decrease in mortality induces agents to substitute human capital for physical capital, by the mechanism mentioned in the previous paragraph. This shift in assets not only improves human capital, but also weakens the dilution effect, because physical capital is more vulnerable to the dilution effect than is human capital.4 Second, a decrease in mortality raises the average age of the working population. Since older workers have more human capital, because of human capital accumulation, such a change in the age composition of the workforce increases the average amount of human capital in the workforce. In the determination of per-capita output, the human capital improvement effect acts in the opposite direction to the physical capital dilution effect. Our model predicts that a decrease in mortality is more likely to increase GDP per capita in an economy with more education (and more resources) because the human capital improvement effect dominates the dilution effect, while the opposite is true in an economy with less education (and fewer resources). Fig. 1 depicts the wage profiles of workers in high- and low-education countries, illustrating the intuition behind our mechanism.5 If the wage rate reflects the amount of human capital, the wage profile represents human capital accumulation (through education, experience, and training, etc.) over a lifetime. The wage profile for high-education countries is steeper

1 Galor and Moav (2004) focus on a different asymmetry between physical and human capital: in contrast to physical capital, human capital is inherently embodied in people, and human capital investment exhibits diminishing returns at the individual level. Based on this asymmetry, they show that income inequality, through capital-market imperfections, affects economic growth differently in the various stages of the development process. 2 Hazan (2009) finds that in developed countries, the expected lifetime working hours for males has decreased because of a decrease in hours worked per year and early retirement, superficially casting doubt on the Ben-Porath effect in economic development. However, this important fact reported by Hazan (2009) does not deny the workings of the Ben-Porath effect because he does not address the causal effect of the expected lifetime working hours on education, and does not consider other possible factors affecting the relationship between labor supply and education (e.g., changes in pension system). The empirical analyses of Jayachandran and Lleras-Muney (2009) and Fortson (2011) show that longer life expectancy increases educational attainment. 3 The conventional channel focuses on the individual return on investment of human and physical capital, whereas our channel focuses on the family return. The relative importance of our channel depends on how important bequest motives are in asset allocation. De Nardi (2004) argues that bequest motives are needed to explain the very skewed wealth distribution observed in U.S. data. Love (2010) suggests that marital status and children are important to understanding portfolio decisions. Inkmann and Michaelides (2012) find evidence supporting the presence of a bequest motive based in U.K. micro data. The results of these studies suggest the importance of our channel. In our model, bequest motives are based on family member altruism. The presence of altruism has been shown by many studies and is assumed in a large number of growth theories (e.g., Loury, 1981; Galor and Zeira, 1993). 4 The following example captures the vulnerability of physical capital to the dilution effect. Suppose that parents leave $10,000 to their two children. There are two measures of asset maintenance, physical and human capital investment, both of which have the same gross rates of return, 100%. First, consider the case where $10,000 is invested in physical capital. If the two children survive, each child gets physical capital of $5,000. If one child dies, the other gets physical capital of $10,000. Next, consider the case where $10,000 is invested in human capital. If both children survive, each child gets human capital of $5,000. If one child dies, the other gets human capital of $5,000. The value of the assets per capita halves by the dilution effect when it is invested in physical capital, but does not change when invested in human capital because human capital is embedded in individuals and disappears with their death. 5 The classification between high- and low-education countries is based on the empirical result in Section 3 and is the same as the classification in panel (b) of Fig. 4. However, owing to limited data availability, the sample in Fig. 1 consists of 15 out of the 47 countries used in the empirical analysis.

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Fig. 1. Wage profile in high- and low-education countries. Source: Lagakos et al. (2018).

and has a higher peak than that for low-education countries, implying that the gap in human capital between young and adult workers is larger in high-education countries. A decrease in mortality has two effects: a direct effect and a composition effect. First, it lifts the profile from the low-education type to the high-education type by increasing educational investment. This directly improves the average amount of human capital because each agent has more human capital. Second, it shifts the weight on the workforce from young to adult workers and, thus, has the effect of improving the average amount of human capital. This composition effect is larger in higher-education countries because they have a larger gap in the amount of human capital between older and younger workers. A notable implication of our theory is the heterogeneity in the effects of mortality on per-capita income among countries. The higher the level of education in a country, the more likely it is that a decrease in mortality will increase income per capita. To test this hypothesis, we use the same data and identification strategy as Acemoglu and Johnson (2007), though our approach differs in that we relax the assumption that all countries are in the same growth regime. Using a finite mixture model (FMM) approach, we investigate whether the effects of mortality on per-capita income differ between countries in high- and low-education regimes.6 Cervellati and Sunde (2011a; 2011b) share our motivation to reinterpret the analysis of Acemoglu and Johnson (2007). Cervellati and Sunde (2011b) split the sample of Acemoglu and Johnson (2007) between pre- and post-demographictransition countries based on the classification criteria used in demography literature. They show that improved life expectancy has a negative effect on per-capita GDP in pre-transition countries, but a positive effect in post-transition countries.7 Cervellati and Sunde (2011a) use an FMM approach without imposing any ex-ante classification, obtaining similar results to those of Cervellati and Sunde (2011b). Cervellati and Sunde (2011a; 2011b) base their studies on demographictransition theory in order to investigate the role of population growth in determining the effect of mortality on per-capita income. Here, we focus on the role of education in determining the effect of mortality on per-capita income based on human-capital theory. Since the demographic-transition and human capital theories are two pillars in the literature on long-run growth, our study is a natural development of this literature. The empirical part of our study shows that both education and population growth are important in determining the effect of mortality on per-capita income. The remainder of this paper is organized as follows. Section 2 presents the model and analyses the effect of mortality changes on income per capita. In Section 3, we confront the testable implications of the model with empirical evidence. Section 4 concludes the paper. 2. Model Consider an overlapping generations model in which agents live for at most two periods, youth and adulthood. Some agents die at the beginning of adulthood and cannot enter the labor market in adulthood. The survival rate is ρ ∈ (0, 1).8 In both periods, (surviving) agents inelastically supply one unit of time to the labor market. The efficiency units of labor per unit of time of young agents are normalized to 1 (i.e., the basic level of human capital), while those of adult agents can increase with educational investment in their youth. At the end of the youth period, agents receive an inheritance from

6 See Frühwirth-Schnatter (2006) for details about FMM, and Bloom et al. (2003), Owen et al. (2009), and Cervellati and Sunde (2011a) for applications to growth regressions. 7 Acemoglu and Johnson (2014) and Bloom et al. (2014) discuss the importance of controlling for initial conditions in the estimation of Acemoglu and Johnson (2007). 8 Here, we concentrate on the role of adult mortality. In reality, child mortality as well as adult mortality plays a key role in the determination of life expectancy, but introducing child mortality into our model has only a minor effect on our results.

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their ancestors, which they allocate between savings and an educational investment. Savings and the educational investment increase asset income and labor income in adulthood, respectively. In the second period (adulthood), surviving agents supply their efficiency units of labor and allocate the household’s labor and asset income between their own consumption and transfers to their offspring. The basic unit in our analysis is a household, consisting of a continuum of individuals.9 Household members of the same generation jointly choose their behavior to maximize their joint utility.10 We impose this assumption mainly with couples in mind. In the real world, married couples would make consumption and investment decisions jointly and with concern for the other’s living standards after their own death. The assumptions of joint utility and joint decision-making are intended to capture this reality. 2.1. Production Production occurs according to Cobb-Douglas production technology. The output produced in period t is given by Y t = K tα H t1−α , where K t and H t are the quantities of physical capital and labor (measured in efficiency units), respectively, employed in production, and α ∈ (0, 1) is the capital share of income. The factor markets are competitive and physical capital depreciates fully in one period. The wage rate and the gross rate of return on physical capital are:

w t = (1 − α ) ktα ≡ w (kt ) and R t = αktα −1 ≡ R (kt ) ,

(1)

respectively, where kt ≡ K t / H t is the capital-labor ratio. 2.2. Households There is a continuum of households of measure 1. In every period, a continuum of individuals of measure 1 is born into a household as young members. They survive and enter the labor market in adulthood with probability ρ ∈ (0, 1). Thus, each household supplies 1 + ρ members (i.e., 1 young members and ρ adult members) to the labor market in every period. Since the measure of households is 1, the total workforce size of this economy is 1 + ρ .11 Household members of the same generation jointly choose their behavior to maximize their joint utility. The preferences of generation t (born in t) of household i are defined over consumption per surviving adult member, cti +1 , and transfer per young member, bti +1 . The preferences are given by:

γ ln cti +1 + (1 − γ ) ln bti +1 ,

(2)

where γ ∈ (0, 1) denotes the relative weight given to consumption.12 In period t, generation t of household i receives an inheritance, bti , from generation t − 1 of household i, which is allocated between savings, sti , and education expenditure, eti : sti + eti = bti . The budget constraint of generation t of household i is:





ρ cti +1 + bti +1 = w t +1 + ρ w t +1 hti +1 + R t +1 bti − eti ,

(3)

where hti +1 denotes the efficiency units of labor (i.e., the level of human capital) per adult member. The LHS is the adultperiod expenditure, namely their own consumption and transfers to their offspring. Since ρ of the 1 adult members survive until the time of consumption, their total consumption is ρ cti +1 . On the other hand, since the size of young members is 1,

the total bequest is bti +1 . The RHS is the adult-period wealth: the first, second, and third terms are the wage income earned by young members, the wage income earned by surviving adults, and the return on savings from the previous period, respectively. Note that we assume that adult members control the young members’ wage income. One may argue that this patriarchal assumption does not fit the description of developed countries, though is suitable for some developing nations. However, this assumption is not as restrictive as it may seem. In the real world, people have some degree of control over the wealth of their offspring because the transfer is usually either positive or negative. In this model, the net transfer to

9 This large family assumption simplifies the analysis by removing the idiosyncratic risk of households, but is not conventional in the literature. A more conventional approach for removing the idiosyncratic risk is to introduce insurance markets. In the real world, whether families or markets are more important as an insurance device depends on circumstances (e.g., the development level of insurance markets). Since the key results of this paper do not depend on whether families or markets serve as an insurance device, we choose the large family assumption for simplification. 10 It is generally agreed that the family institution serves as an insurance device for individuals (e.g., Weiss, 1997). For example, Kotlikoff and Spivak (1981) find that consumption and bequest-sharing arrangements in marriages and larger families can significantly substitute for complete and fair annuity markets, suggesting the importance of cooperation among family members in asset formation. 11 It is widely accepted in the literature that fertility plays an important role in human capital investment (e.g., Moav, 2005; Hazan and Zoabi, 2006). However, in order to concentrate on our main mechanism and to exclude the fertility channel, we assume that fertility is fixed exogenously. Note that introducing fertility choice does not qualitatively change our main results because we focus on own choice of education, not parental choice; that is, the so-called quantity-quality mechanism does not work in the portfolio choice between physical and human capital. 12 This type of utility function is often assumed in the literature (e.g., Galor and Zeira, 1993; Galor and Moav, 2004). Our key results do not depend on a particular form of utility function, but this utility function makes it possible to obtain a closed-form solution.

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offspring, bti +1 − w t +1 , can be either positive or negative: the larger the amount of adult members’ human capital, the more likely it is that the net transfer will be positive. Therefore, our model can capture the reality that there is exploitation of child labor in underdeveloped countries, whereas in advanced countries, many people transfer a positive amount of wealth to their children, although they can also leave a debt. Furthermore, this patriarchal assumption simplifies the dynamics because we need not consider the decisions of two generations simultaneously. The level of human capital in adulthood, hti +1 , is a function of the real expenditure on education in childhood t, eti :

hti +1 = 1 + μeti ,

(4)

where μ > 0 represents the efficiency of education. Without capital investment in education, the level of human capital in adulthood is equal to the basic level during youth.13 For analytical convenience, we assume a linear human capital production technology.14 Generation t of household i maximizes (2) subject to (3) and (4). The solution to this problem is given by

eti

=

⎧ ⎨0 ⎩

and

[0, ∞)

∞

if if if

ρμ w t +1 < R t +1 , ρμ w t +1 = R t +1 , ρμ w t +1 > R t +1 ,





(5)





bti +1 = (1 − γ ) w t +1 + ρ w t +1 1 + μeti + R t +1 bti − eti

 .

(6)

˜ below which households do not invest in human capital. That is, k˜ There is a threshold level of the capital-labor ratio, k, is defined by ρμ w (k˜ ) = R (k˜ ). It follows from (1) that k˜ = α / [(1 − α ) ρμ]. If the capital-labor ratio in the next period is ˜ households do not invest in human capital. expected to be below k, Before moving to the equilibrium analysis, we should mention two points. First, the optimal level of human capital investment depends on the rate of return and is independent of the level of income. Since there are no credit constraints in this model, the rate of return is the investor’s only concern. Second, as mortality declines, households are more likely to invest in human capital (i.e., k˜ decreases with ρ ). Since human capital is inherently embodied in people, it yields returns in adulthood for surviving members only, whereas physical capital does not have this property. With higher mortality, the larger part of human capital acquired by households comes to nothing. Thus, human capital investment becomes more profitable compared to physical capital investment as mortality declines. 2.3. Aggregate physical and human capital Assume that all households have identical initial wealth. We then focus on a symmetric equilibrium, where sti = st and eti = et , for all t and i.15 Given the inheritance received by the households of generation t, the optimization of these households in period t determines the level of physical capital, K t +1 , and human capital, H t +1 , in period t + 1: K t +1 = st = bt − et and H t +1 = 1 + ρ (1 + μet ). It follows that the capital-labor ratio in period t + 1 is:

kt +1 =

bt − e t 1 + ρ (1 + μet )

.

(7)

˜ Since et = 0 in this case, kt +1 = First, suppose that the capital-labor ratio in the next period is expected to be below k. ˜ that is, bt / (1 + ρ ). The resultant capital-labor ratio is consistent with households’ expectations if and only if bt / (1 + ρ ) ≤ k; bt ≤

α (1 + ρ ) ≡ b˜ . (1 − α ) ρμ

(8)

˜ on the other hand, et > 0. Note that when et > 0, kt +1 = k˜ must hold. If kt +1 < k, ˜ then no one invests In the case of bt > b, ˜ then no one invests in physical capital and, thus, kt +1 = 0, which is inconsistent in human capital (i.e., et = 0). If kt +1 > k, ˜ When et > 0, using (7) and kt +1 = k, ˜ we obtain et = [(1 − α ) ρμbt − α (1 + ρ )] / (ρμ). Therefore, we can with kt +1 > k. write the equilibrium educational investment as a function of bt : 13 We are aware that opportunity and pecuniary costs constitute a major part of education costs in the real world (e.g., Bils and Klenow, 2000), and that time devoted to education is important to determining educational attainment. However, following the spirit of Galor and Moav (2004), we assume there is no difference in the time agents devote to education, enabling us to concentrate on the portfolio choice between physical and human capital investments. 14 If we assume a strictly concave human capital production technology, perpetual growth (Pattern III in Fig. 2) does not arise. However, all comparativestatic results in Propositions 1 and 2, except for those in the balanced growth path, still hold. Since the emergence of perpetual growth is not essential in this study, we assume linear technology to obtain a closed-form solution. 15 It is also possible that some households specialize in physical capital accumulation and others specialize in human capital accumulation, and that the ratio between the two is determined in equilibrium. However, our results do not change in such a situation because the aggregate variables in the asymmetric equilibrium are the same as those in the symmetric equilibrium, by households’ arbitrage behavior.

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Fig. 2. Dynamics.

et =

0

(1−α )ρμbt −α (1+ρ )

ρμ

if bt ≤ b˜ , if

bt > b˜ .

This implies that a higher ρ and a larger bt induce a larger educational investment. Although the level of inheritance does not affect the investment decision at the household level, it matters at the aggregate level because of the generalequilibrium effect: the greater the resources available, the higher the level of human capital investment, such that the marginal returns on physical and human capital are equalized. Then, it follows from (1), (6), and (7) that the evolution of inheritance is:

bt +1 (bt ) =

(1 − γ ) (1 + ρ )1−α btα ≡ 1 (bt )

if bt ≤ b˜ ,

(1 − γ ) α α (1 − α )1−α ρ −α μ−α (1 + ρ + ρμbt ) ≡ 2 (bt ) if bt > b˜ .

(9)

If the initial value of bt is given, the subsequent behavior of this economy is completely specified by this difference equation. The equation (9) implies that 1 (b˜ ) = 2 (b˜ ), 1 (b˜ ) = 2 (bt ), bt +1 (0) = 1 (0) = 0, bt +1 (bt ) > 0, bt +1 (0) = 1 (0) = ∞,

˜ and b (bt ) = 0 if bt > b. ˜ Therefore, depending on the parameter configuration, we can classify bt+1 (bt ) < 0 if bt ≤ b, t +1 the dynamic system into three patterns (see Fig. 2). In Pattern I (panel (a)), there exists a steady state where physical capital investment is the only method of capital accumulation. In Pattern II (panel (b)), there exists a steady state with both physical and human capital investments. In Pattern III (panel (c)), the economy shows persistent growth, and both physical and human capital investments exist along the growth path. The steady-state inheritances in Patterns I and II (the fixed points of 1 (·) and 2 (·), respectively) are given by:

⎧ ⎨ b∗ = (1 − γ ) 1−1 α (1 + ρ ) 1

in Pattern I,

⎩ b∗ =

in Pattern II.

2

(1−γ )α α (1−α )1−α ρ −α μ−α (1+ρ ) 1−(1−γ )α α (1−α )1−α ρ 1−α μ1−α

˜ For Pattern II to arise, b∗ > b˜ and  (bt ) = (1 − γ ) α α (1 − α )1−α ρ 1−α μ1−α < 1. For Pattern III For Pattern I to arise, b∗1 ≤ b. 1 2  to arise, 2 (bt ) ≥ 1.

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According to the value of the survival rate, economy are classified as

⎧ ⎨ Pattern I

if if if

Pattern II ⎩ Pattern III where ρ˜1 ≡

109

ρ , the main parameter of interest, the patterns of the dynamics of this

ρ ≤ ρ˜1 , ρ˜1 < ρ ≤ ρ˜2 , ρ˜2 < ρ , α

α 1

(1 − γ ) 1−α (1 − α ) μ

and ρ˜2 ≡

α − 1−α 1

(1 − γ ) 1−α (1 − α ) μ

.

(10)

˜ Thus, a decrease in mortality increases the steady-state An increase in ρ shifts 1 (·) and 2 (·) upward and decreases b. value of bt , if it exists. Otherwise, it increases the growth rate of bt . Panel (d) in Fig. 2 illustrates this effect. Which pattern arises ultimately depends on the return on education. A higher return on education induces households ˜ and enables households to to substitute human capital for physical capital, decreasing the threshold level of inheritance, b, accumulate more wealth, shifting bt +1 (bt ) upward. Thus, Patterns I, II, and III correspond to economies with low, medium, and high returns on education, respectively. Since an increase in the survival rate, ρ , means a higher return on education, the effects of increases in ρ are depicted by Panel (d) in Fig. 2. An increase in the productivity parameter in education, μ, has a similar effect because it directly raises the return on education. 2.4. Effects of mortality changes on per-capita output It follows from the results obtained in the previous subsection that given bt , bt +1 increases with ρ (see panel (d) in Fig. 2). Then, what about the effect on per-capita output? The answer is not clear, because a higher survival rate increases the population and dilutes physical capital per capita. This subsection attempts to answer this question. Suppose there arises a once-off and permanent rise in ρ in period τ . Our analysis distinguishes between the short- and long-run effects of mortality changes on per-capita output. The short- and long-run effects refer to the effects on per-capita output of the current period, y τ , and per-capita output in the steady state, y ∗ (or its growth rate, ( yt +1 − yt ) / yt , on the balanced growth path), respectively. Here, we impose an additional assumption:

α<

1 1+ρ

(11)

,

which means that human capital makes a sufficiently large contribution to production. This assumption seems empirically reasonable. The value of 1/ (1 + ρ ) is in [1/2, 1] because the value of ρ is in [0, 1], whereas it is widely accepted that the capital share, α , is less than 1/2. We begin with the short-run effect. This effect varies depending on whether a change in the survival rate is previously expected or not. If the change is expected, K τ and hτ are optimally chosen by households for a given amount of bτ −1 . If the change is unexpected, households become aware of the change after K τ and hτ are determined. The difference between the expected and unexpected cases is that bτ −1 is given in the expected case while K τ and hτ are given in the unexpected case. We obtain the following proposition for the short-run effect of a change in the survival rate on per-capita output. Proposition 1. The short-run effect: (i) If an increase in ρ is not expected, it increases per-capita output if and only if hτ > 1/ [1 − α (1 + ρ )]. Since 1/ [1 − α (1 + ρ )] is larger than 1, the effect is positive only if the level of human capital is larger than ˜ it decreases perthe basic level. (ii) If an increase in ρ is expected, (A) in the case without human capital investment (i.e., bτ −1 ≤ b), ˜ the effect on per-capita output is positive if capita output, and (B) in the case with positive human capital investment (i.e., bτ −1 > b), and only if bτ −1 > α (1 + ρ )2 /{ρμ [1 − α (1 + ρ )]}. Proof. (i) Given K τ and hτ , the output per capita in period

yτ =

K τα H τ1−α 1+ρ

=

K τα (1 + ρ hτ )1−α

The effect of an increase in

1+ρ

τ , y τ ≡ Y τ / (1 + ρ ), is

.

ρ on y τ is

∂ yτ [1 − α (1 + ρ )] hτ − 1 = K τα (1 + ρ hτ )−α . ∂ρ (1 + ρ )2 This is positive if and only if hτ > 1/ [1 − α (1 + ρ )] (>1). (ii) Given bτ −1 , the output per capita in period τ is



yτ =

[bτ −1 / (1 + ρ )]α

if bτ −1 ≤ b˜ ,

α α (1 − α )1−α μ−α (1 + ρ + ρμbτ −1 ) / [(1 + ρ ) ρ α ]

if

bτ −1 > b˜ .

(12)

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˜ (A) It follows that ∂ y τ /∂ ρ < 0 when bτ −1 ≤ b. ˜ (B) When bτ −1 > b, we obtain the following:



∂ yτ α α (1 − α )1−α (1 + μbτ −1 ) (1 + ρ ) ρ α − (1 + ρ + ρμbτ −1 ) ρ α + α (1 + ρ ) ρ α −1 = , ∂ρ μα [(1 + ρ ) ρ α ]2

(13)

and

∂ 2 yτ α α (1 − α )1−α μ1−α [1 − α (1 + ρ )] = . ∂ b τ −1 ∂ ρ (1 + ρ )2 ρ α Under assumption (11), ∂ 2 y τ /∂ bτ −1 ∂ ρ > 0: a higher value of ρ is more likely to increase per-capita output as bτ −1 rises. We denote the inheritance level such that a change in ρ has no effect on per-capita output by bˆ (i.e., ∂ y τ (bˆ )/∂ ρ = 0). ˜ Therefore, when bτ −1 > b, ˜ Using (13), we obtain bˆ = α (1 + ρ )2 /{ρμ [1 − α (1 + ρ )]}. We can easily confirm that bˆ > b. ˆ 2 ∂ y τ /∂ ρ > 0 if and only if bτ −1 > b. First, consider the effect of the unexpected change. Since K τ and hτ are given, an increase in ρ affects per-capita output in period τ , K τα H τ1−α / (1 + ρ ) = [K τ / (1 + ρ )]α [H τ / (1 + ρ )]1−α , through two channels. One is the negative dilution effect on physical capital, which impinges on physical capital per capita, K τ / (1 + ρ ). More people survive while the aggregate physical capital is fixed, reducing physical capital per capita. The other is the positive composition effect on human capital, which impinges on the average level of human capital, H τ / (1 + ρ ). An increase in ρ increases the relative number of adult workers to young workers. If hτ is larger than 1, it increases the average quality of human capital in the workforce, increasing per-capita output. This effect becomes greater as hτ becomes larger. Therefore, if hτ is sufficiently large, the positive composition effect dominates the negative dilution effect. Second, consider the effect of the expected change. In contrast to the unexpected case, each household optimally reacts ˜ to the change in ρ . However, when physical capital investment is the only method of capital accumulation (i.e., bτ −1 ≤ b), there is no practical difference from the unexpected case because households do not increase human capital in response to such a change. Since bτ −1 is given, the assets available to the generation with declining mortality do not change. Therefore, as a result of the decrease in mortality, more people survive, while the aggregate physical capital does not change and, thus, ˜ the effect is positive if the per-capita output decreases. In the case with positive human capital investment (i.e., bτ −1 > b), ˜ bτ −1 is sufficiently large. The intuition behind this result is as follows. As in the case of bτ −1 ≤ b, a decrease in mortality ˜ a increases the population and decreases the return per unit of human capital. However, in contrast to the case of bτ −1 ≤ b, decrease in mortality increases the average amount of human capital in the labor market, 1/ (1 + ρ ) × 1 + ρ / (1 + ρ ) × hτ , which is the weighted average of the young and adult agents’ human capital, through two channels. First, an increase in ρ induces households to invest in human capital (i.e., ∂ e τ −1 /∂ ρ > 0) and, thus, hτ increases. Second, an increase in ρ raises the proportion of adult workers, ρ / (1 + ρ ), in the workforce. Since adult workers have more human capital than young workers do (i.e., hτ > 1), an increase in the proportion of adult workers increases the average amount of human capital. Therefore, the negative effect on physical capital and the positive effect on human capital coexist, and thus the total effect can be either positive or negative. If bτ −1 is large, then the educational investment is large, in which case the growth rate of human capital from youth to adulthood is high. Then, the higher weight of adult human capital resulting from the increase in ρ has a greater effect on increasing the average amount of human capital. Therefore, as bτ −1 increases, a higher value of ρ is more likely to make the positive effect dominant. Next, we obtain the following proposition with regard to the long-run effect of a change in the survival rate on per-capita output. Proposition 2. The long-run effect: (i) In Pattern I, an increase in ρ has no effect on per-capita output; (ii) in Pattern II, an increase in ρ increases per-capita output; and (iii) in Pattern III, an increase in ρ raises the growth rate of per-capita output. α

Proof. (i) In Pattern I, the output per capita in the steady state is y ∗ ≡ Y ∗ / (1 + ρ ) = (1 − γ ) 1−α . It follows that ∂ y ∗ /∂ ρ = 0. (ii) In Pattern II, the output per capita in the steady state is

y∗ = This implies

α α (1 − α )1−α . ρ α μα − (1 − γ ) α α (1 − α )1−α ρμ

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∂ y∗ α α +1 (1 − α )1−α ρ α −1 μα  (ρ ) = −

2 , ∂ρ ρ α μα − (1 − γ ) α α (1 − α )1−α ρμ where  (ρ ) ≡ 1 − (1 − γ ) α α −1 (1 − α )1−α ρ 1−α μ1−α . Note that  (ρ ) < 0 and  ρ˜1 = 0. Since we now consider the case of ρ > ρ˜1 , we obtain ∂ y ∗ /∂ ρ > 0. (iii) In Pattern III, since there is no steady state, we analyze the long-run growth rate instead. From (9) and (12), we obtain the following per-capita output growth rate:

y t +1 − y t yt

= (1 − γ ) α α (1 − α )1−α ρ 1−α μ1−α −

ρμbt −1 . 1 + ρ + ρμbt −1

Since bt grows persistently, bt −1 → ∞ as t → ∞. Thus, in the long run, the growth rate converges to (1 − γ ) α α (1 − α )1−α ρ 1−α μ1−α − 1, which increases with ρ . 2 In the long run, in contrast to the fixed inheritance (or the fixed human and physical capital) in the short run, the future generation’s inheritance (and, thus, the future generation’s human and physical capital) increases because an increase in the survival rate increases labor inputs and, thus, output. This effect offsets the diluting effect of an increase in the population size. Since physical capital per capita does not decrease, the output per capita does not decrease, even if there is no positive effect on human capital investment. In the case with positive human capital investment, an increase in the survival rate necessarily increases the output per capita by enhancing human capital investments. In summary, the above analysis generates the following predictions: (i) the effect of a decrease in mortality on per-capita output is ambiguous; (ii) the higher the initial education level, the more likely it is that an unexpected decrease in mortality will increase output per capita in the short run; (iii) the larger the initial inheritance from the previous generation, the more likely it is that an expected decrease in mortality will increase output per capita in the short run; and (iv) the effect of a decrease in mortality on per-capita output is more likely to be positive in the long run than it is in the short run. 2.5. Numerical illustration This subsection presents numerical examples to illustrate our key results. The value of physical capital share, α , is set to 1/3 because it is well known that capital share of income is roughly 1/3. Based on the analysis of Alvaredo et al. (2017), we set the relative weight on own consumption, γ , to 0.9.16 The productivity parameter in education, μ, is chosen to ensure that the pattern switch occurs at a reasonable survival rate. According to the classification between high- and low-education countries in the empirical part of this paper (Section 3), the high- and low-education countries respectively had an average life expectancies of 58.20 and 43.77 years in 1940. Suppose that the length of a period in the model is 20 years, and thus an agent lives for 20 years as a child, for 20 years as a young, and for 20 years as an adult. Then, the survival rates, ρ , corresponding to the average life expectancies of 58.20 and 43.77 are 0.91 and 0.19, respectively. We set μ to 28.78 so that the threshold survival rate given by (10), ρ˜1 , is equal to the average of 0.91 and 0.19, that is, 0.55. Comparison among economies with different ρ ’s We demonstrate how a once-off and permanent increase in the survival rate, ρ , affects per-capita output. Suppose that the economies are in steady states, with ρ = 0.4, ρ = 0.5, and ρ = 0.6, in t = 0. We increase the value of ρ from 0.4 to 0.5, from 0.5 to 0.6, and from 0.6 to 0.7 in t ≥ 1. Since ρ˜1 (the threshold survival rate between Patterns I and II) is 0.55, the economy with an initial survival rate of 0.4 is in Pattern I, both before and after the change; the economy with an initial survival rate of 0.5 switches from Pattern I to Pattern II as a result of the change; and the economy with an initial survival rate of 0.6 is in Pattern II, both before and after the change. Panel (a) in Fig. 3 depicts the responses in per-capita output in these simulations. The labels “Expected” and “Unexpected” refer to the cases where the changes in ρ are expected by the young in t = 0 and they are not, respectively. The per-capita output steeply decreases immediately after the change owing to the dilution effect on physical capital. Subsequently, per-capita output starts increasing owing to the physical capital accumulation by the larger working population, returning to the initial steady-state level in Case 1. Per-capita output increases further because of the increases in the average amount of human capital, converging to the new steady-state levels above the initial levels in Cases 2 and 3. The effects of the expected and unexpected changes are similar. In Case 1, there is no difference between the effects of the expected and unexpected changes. This is because physical capital investment is the only method of capital accumulation and, thus, households do not change their asset allocation, irrespective of whether the change is expected. The difference arises in Cases 2 and 3, but is only quantitative. The negative effect on per-capita output is stronger in the case of an unexpected change because households do not react optimally in response to a mortality change. Therefore, the per-capita output decreases more sharply and converges to the new steady-state level more slowly in the case of the unexpected change.

16 Alvaredo et al. (2017) report that in some Western countries, the share of annual flow of bequests and gifts in national income in 1940 was about 10%, implying that the relative weight on the transfer to offspring, 1 − γ , is 0.1.

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Fig. 3. Simulation results.

Comparison among economies with different μ’s Next, we examine the differential effects of mortality changes between economies with different education systems. We model the development of an education system as an increase in μ: a higher value of μ implies a more efficient education system. Here, we examine the responses in per-capita output to mortality changes for different values of μ, along with the same values of α and γ used above. Suppose that the economies are in steady states, with μ = 10, μ = 30, and μ = 50, in t = 0. From (10), then, the respective threshold survival rates between Patterns I and II are 1.58, 0.53, and 0.32. We increase the value of ρ from 0.45 to 0.75 in t ≥ 1. The economy with μ = 10 is in Pattern I, both before and after the change; the economy with μ = 30 switches from Pattern I to Pattern II as a result of the change; and the economy with μ = 50 is in Pattern II, both before and after the change. Panel (b) in Fig. 3 displays the responses of per-capita output in these simulations. As in panel (a), the labels “Expected” and “Unexpected” refer to

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the cases where the changes in ρ are expected by the young in t = 0 and they are not, respectively. The per-capita output decreases steeply immediately after the change owing to the dilution effect on physical capital. Subsequently, it starts increasing, returning to the initial steady-state level in Case 1 and converging to the new steady-state levels above the initial levels in Cases 2 and 3. The mechanisms behind these dynamics and the difference between the effects of the expected and unexpected changes are the same as those of the simulations with different ρ ’s. Panels (a) and (b) in Fig. 3 capture the feature that we want to emphasize. The initial education level matters for determining the effect of mortality changes on per-capita output. Regardless of the cause of lower education levels (i.e., lower ρ or lower μ), an increase in the survival rate is more likely to have a negative effect on per-capita output in an economy with less education (and fewer resources): the size of the initial drop is larger, the pace of the subsequent recovery is slower, and the steady-state level attained finally is lower.17

3. Empirical analysis

A notable implication of our theory is heterogeneity in the effects of mortality on per-capita income among countries. It follows from Proposition 1 that when the mortality change is not expected, the initial education level determines whether the effect is positive or negative in the short run. According to this theoretical result, we test the hypothesis that a higher initial education level increases the likelihood that a decrease in mortality will increase income per capita. The reason why we choose this hypothesis from several testable implications is its compatibility with our data. Our estimation period is the 40 years between 1940 and 1980, which would be much closer to the short run in the model than it would to the long run, because a longer period is required for the dynamics to converge.18 Furthermore, we exploit an exogenous event of mortality change that can be considered to have been previously unexpected for many people.

3.1. Empirical framework and identification

The dependent variable is the change in log GDP per capita, and the main explanatory variable is the change in predicted mortality. Our estimations are based on the following estimation framework:

ln y i = C + π mi + i , where ln y i and mi are the changes in log GDP per capita and the (instrumented) predicted mortality of country i between 1940 and 1980, respectively.19 Following Cervellati and Sunde (2011a), we use the change in predicted mortality rather than life expectancy as the regressor. Note that a negative coefficient π implies that a decrease in mortality promotes growth. To estimate the causal effect of mortality on per-capita income, we follow the identification strategy proposed by Acemoglu and Johnson (2007). The instrument for the change in mortality is the reduction in mortality from 15 infectious diseases (e.g., tuberculosis, malaria, and pneumonia), following the international epidemiological transition in the 1940s.20 The basic idea behind this choice of instrument is as follows.21 There were no appropriate treatments for these diseases in1940, and the international epidemiological transition enabled the worldwide dissemination of treatment and prevention by 1980. Thus, the change in mortality resulting from these diseases between 1940 and 1980 was exogenous to each country and, thus, we can assume that the exclusion restriction holds.

17

Here, we assume a parameter configuration such that the per-capita output decreases in the short run in response to an increase in

ρ (i.e., the initial

values of bt and ht are smaller than bˆ and 1/ [1 − α (1 + ρ )], respectively). For a simulation of Case 3, where an economy is initially in Pattern II, we can also choose a parameter configuration that makes the short-run effect positive, as shown in Proposition 1. 18 If the length of one period in the model corresponds to 20 years in the real world, the 40-years estimation period corresponds to two periods in the model. The simulation results in Fig. 3 suggest that two periods are too short for the economy to converge to a new steady state. 19 Here, we focus on the effect of mortality on per-capita GDP, which is of our main interest. Appendix A explores whether other related variables behave consistently with the theory in the corresponding period. 20 The international epidemiological transition consists mainly of three factors: a wave of global drug and chemical innovations, the establishment of the WHO and UNICEF, and the change in international values leading to a fast dissemination of medical knowledge. The transition caused a dramatic improvement in life expectancy in much of the world, particularly in less developed areas. 21 See Acemoglu and Johnson (2007) for more detail.

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The departure from Acemoglu and Johnson (2007) is that we relax the assumption that all countries are in the same growth regime in order to allow for heterogeneous effects of mortality on per-capita income between regimes. For this purpose, we use a finite-mixture approach, jointly estimating the probability of being in a distinct growth regime and the effect of mortality changes in each regime. Compared with the approach that assigns observations into groups a priori, our approach has the advantage of being data driven, because we estimate the country groupings into regimes and the growth regression parameters for each regime. We assume that growth processes can be classified into two discrete regimes.22 We refer to these as “Low” and “High.” As will become apparent later, a variable related to education level is a significant predictor of regime membership. The labels “Low” and “High” refer to low- and high-education regimes, respectively. The probability structure for a given country is:



f

     ln y | m; π Low , π High , φ Low , φ High = φ Low f ln y | m; π Low + φ High f ln y | m; π High ,

where φ j is the probability of membership in latent regime j, and f ln y | m; π j conditional on membership in latent regime j. The probabilities are parameterized as:

φ Low =

exp (θ X ) 1 + exp (θ X )

and φ High =

1 1 + exp (θ X )

is the distribution of growth rates

,

where X represents the determinants of regime membership, and θ is the coefficient that captures the effect of X on the probability of being in the Low regime. Based on the prediction derived in the theoretical part, we use the initial level of education as membership predictors X (see (i) in Proposition 1). In order to draw accurate conclusions about country characteristics that sort countries into regimes, we should use membership predictors that are uncorrelated with the error term in the growth model. Whether the initial level of education can be seen as exogenous depends on whether the mortality change is unexpected. It seems reasonable to assume that people who had already completed their education by the onset of the international epidemiological transition (e.g., people over 30 years of age in 1950) did not expect it when they received education. We estimate the model using the maximum likelihood method. Assume that the error term in the growth equation comes from a normal distribution, with standard deviation σ j . The log-likelihood function is:

ln L =

N        ln φ Low f ln y i | mi ; π Low + φ High f ln y i | mi ; π High , i =1

where

 f

ln y i | mi ; π

j





1

= 2π



σj

ln y i − C j − π j mi exp − 2

2 j 2

2  .

σ

We estimate this finite mixture model using the Stata package fmm (Deb, 2012). 3.2. Data The dependent variable is the change in log GDP per capita between 1940 and 1980, and the main explanatory variable is the change in predicted mortality between 1940 and 1980. We use Maddison (2003) and Acemoglu and Johnson (2007) as data sources for these variables. We use the same base sample of 47 countries as in Acemoglu and Johnson (2007), for which all relevant data on these variables are available for 1940 and 1980. We use education level as a predictor of regime membership. Specifically, we use variables related to tertiary education as education measures. Recall that our theory addresses agents’ decisions about their own education, rather than education provided by parents. It is reasonable to focus on variables related to higher levels of education, for consistency with the theory. Further, we check robustness using the proportion of no-schooling among persons as another measure of education. The data on education come from Barro and Lee (2013). This study focuses mainly on the role of education in the heterogeneous effects of mortality on income per capita, based on human capital theory, though other studies focus on the role of population growth, based on demographic-transition theory (Cervellati and Sunde, 2011a; 2011b). Our baseline estimations only use variables related to education as regimemembership predictors, but we also estimate models that include variables related to both education and population as

22 Although it is possible to assume more than two regimes, we select the two-regime model for both theoretical and empirical reasons. From a theoretical point of view, the characteristics of our model economy differ between the two regimes, namely the regime where only physical capital is accumulated and the regime where both physical and human capital are accumulated. From a empirical point of view, as a result of conducting the likelihood-ratio test for each FMM specification, we have confirmed that the three-regime model does not significantly improve the likelihood value relative to the two-regime model.

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Table 1 Summary statistics. Variables

Obs.

Mean

Std. Dev.

Change of log GDP per capita (1940–1980) Change of predicted mortality (1940–1980) Years of tertiary schooling: 30–39 (1950) Years of tertiary schooling: 30–49 (1950) Tertiary complete (%): 30–39 (1950) No schooling (%): 30–39 (1950) Log of GDP per capita (1940) Change of log population (1930–1940)

47 47 47 47 47 47 47 47

0.884 −0.473 0.095 0.090 1.824 32.685 7.739 0.130

0.388 0.280 0.124 0.115 2.380 29.410 0.725 0.072

Min

Max

−0.086 −1.126 0.002 0.001 0.038 0.2 6.332 −0.015

1.606 −0.121 0.604 0.548 11.957 86.7 8.855 0.303

regime-membership predictors for comparison with previous studies. Our data source for the population variables is Maddison (2003). Table 1 provides the summary statistics. 3.3. Results and implications Table 2 presents the main estimation results. The results reported in column [1] are qualitatively the same as the results obtained in Acemoglu and Johnson (2007). With the full sample, the effect of mortality on income per capita is positive (a positive coefficient of predicted mortality change); that is, the effect of life expectancy on income per capita is negative. Columns [2]–[9] present estimates of the finite mixture models. In columns [2] and [3], as the baseline estimation, we use the average number of years of tertiary schooling in the population between the ages of 30 and 39 in 1950 as covariate X in order to predict the latent regime membership. Since people over 30 years of age in 1950 completed their education by the onset of the international epidemiological transition, it seems reasonable to use a measure of tertiary schooling in the population between the ages of 30 and 39 in 1950 as the covariate. The estimates in columns [2] and [3] indicate the existence of two different regimes, with opposite effects of mortality on income growth. Countries with a higher level of education are less likely to be classified to the Low regime (a negative coefficient of covariate). A decrease in mortality tends to increase income per capita in the High regime (a negative coefficient of predicted mortality change) and decrease income per capita in the Low regime (positive coefficient). This result is consistent with our theory. In the estimations reported in columns [4]–[9], we use different education criteria to those used in columns [2] and [3] as predictors of regime membership in order to check the robustness of our results. The estimations reported in columns [4] and [5] use the average number of years of tertiary schooling in the population between the ages of 30 and 49, rather than between 30 and 39, as covariates.23 The estimations reported in columns [6] and [7] use the proportion of the population that completed tertiary education, rather than the average number of years of tertiary schooling, as covariates. The estimations reported in columns [8] and [9] use the proportion of no schooling among persons as covariates. The results reported in columns [4]–[9] demonstrate that the choice of measures of education has only minor effects compared to the main finding of heterogeneous effects of mortality on growth. Fig. 4 intuitively captures the difference between our results and those of Acemoglu and Johnson (2007). Panel (a) in Fig. 4 shows that in the full sample, as reported by Acemoglu and Johnson (2007), a decrease in mortality depresses income per capita. In panel (b) in Fig. 4, we assign countries to two groups, based on the estimations in columns [2] and [3] in Table 2. In the first group, the countries have an estimated probability of being in the “High” regime of more than 50% (High group), and the second group consists of all other countries (Low group). It follows from panel (b) in Fig. 4 that a decrease in mortality boosts income per capita in the High group, but depresses income per capita in the Low group. One may argue that the effect of education only captures the effect of GDP per capita, and that our estimation results suggest that the degree of economic development, not education, influences the effect of mortality on per-capita income. We conduct the estimation reported in columns [1] and [2] in Table 3 to address this problem. In addition to the education criterion, the estimation uses log GDP per capita in 1940 as a covariate. The result shows that education remains a significant predictor of regime membership, after controlling for the effect of GDP per capita, whereas log GDP per capita is not a significant predictor, after controlling for the effect of education. The estimation reported in columns [3] and [4] in Table 3 uses education criteria and demographic criteria as predictors of regime membership. The result shows that both criteria are significant predictors of regime membership. Countries with higher levels of education and lower population growth are more likely to be classified into the regime in which a decrease in mortality increases income per capita. This is consistent with the results of Cervellati and Sunde (2011a; 2011b). The estimates are quantitatively similar across specifications. Overall, the findings support our hypothesis that education level plays an important role in the heterogeneous effects of mortality on income per capita, even after controlling for the effects of income level and demographic factors.

23 The results are qualitatively unchanged when we use the education measures of the older age groups (between 40 and 49, 50 and 59, and 40 and 59) in 1950 as covariates.

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Table 2 Estimation results I. Finite Mixture Model Years of tertiary

Age group

30–39

Regime [1]

Low [2]

High [3]

Low [4]

High [5]

Low [6]

High [7]

Low [8]

High [9]

0.585∗∗∗ [0.147] 1.160∗∗∗ [0.069]

0.574∗∗∗ [0.207] 1.052∗∗∗ [0.213]

−0.525∗ [0.315] 1.014∗∗∗ [0.081]

0.590∗∗∗ [0.224] 1.071∗∗∗ [0.253]

−0.532 [0.332] 1.007∗∗∗ [0.080]

0.559∗∗ [0.242] 1.033∗∗∗ [0.269]

−0.497 [0.330] 1.022∗∗∗ [0.087]

0.495∗∗∗ [0.143] 0.972∗∗∗ [0.163]

−0.445 [0.419] 1.068∗∗∗ [0.070]

0.163∗∗∗ [0.034]

0.341∗∗∗ [0.08]

0.159∗∗∗ [0.041]

0.332∗∗ [0.08]

0.163∗∗ [0.038]

0.311∗∗∗ [0.069]

Predicted mortality change Constant Probability of regime High

0.335∗∗∗ [0.064]

σ Coefficient of covariate Constant AIC BIC SABIC Number of countries

47

Tertiary complete 30–49

0.338

−17.537∗∗ [7.032] 2.154 [1.332] 42.452 57.254 32.163 47

No schooling

30–39

0.324

−18.879∗∗ [9.329] 2.286 [1.951] 42.365 57.166 32.075 47

30–39

0.357

−1.077∗∗ [0.430] 2.274 [1.525] 41.37 56.172 31.081 47

0.362

0.041∗ [0.022] −0.548 [1.081]

0.156∗∗∗ [0.061]

40.214 55.015 29.924 47

OLS (column [1]) and FMM with two components (columns [2]–[9]). All regressions are long-difference specifications, with two observations per country (i.e., 1940 and 1980). The dependent variable is the log of GDP per capita. The independent variable is predicted mortality. The regression reported in columns [2] and [3] uses years of tertiary schooling between ages 30 and 39 in 1950 as covariates. The regression reported in columns [4] and [5] uses years of tertiary schooling between ages 30 and 49 in 1950 as covariates. The regression reported in columns [6] and [7] uses tertiary schooling completed between ages 30 and 39 in 1950 as covariates. The regression reported in columns [8] and [9] uses no schooling between ages 30 and 39 in 1950 as covariates. The samples correspond to the base sample of Acemoglu and Johnson (2007). AIC, BIC, and SABIC are Akaike, Bayesian, and Sample Adjusted Bayesian information criteria, respectively. Robust standard errors are in brackets, and ∗∗∗ , ∗∗ , and ∗ indicate significance at the 1-, 5-, and 10% levels, respectively.

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OLS Covariate

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Table 3 Estimation results II. Finite Mixture Model Covariate Age group

Years of tertiary/Log of GDP per capita 30–39

Regime

Low [1]

High [2]

Low [3]

High [4]

Predicted mortality change

0.549∗∗∗ [0.207] 1.029∗∗∗ [0.135]

−0.527∗ [0.301] 1.017∗∗∗ [0.070]

0.448∗∗∗ [0.168] 0.971∗∗∗ [0.135]

−0.631∗∗ [0.286] 1.013∗∗∗ [0.070]

0.164∗∗∗ [0.036]

0.335∗∗∗ [0.051]

Constant Probability of regime High

σ Coefficient of covariate Constant AIC BIC SABIC Number of countries

0.332∗∗∗ [0.063]

0.354

−13.323∗ /−0.568 [7.926]/[0.775] 6.176 [5.722]

Years of tertiary/Population Growth 30–39

0.361

−15.049∗ /23.192∗∗ [8.048]/[11.117] −0.803 [1.205]

44.111 60.762 32.535 47

0.155∗∗∗ [0.025]

38.813 55.465 27.237 47

FMM with two components. All regressions are long-difference specifications, with two observations per country (i.e., 1940 and 1980). The dependent variable is the log of GDP per capita. The independent variable is predicted mortality. The regression reported in columns [1] and [2] uses years of tertiary schooling between ages 30 and 39 in 1950 and the log of GDP per capita in 1940 as covariates. The regression reported in columns [3] and [4] uses tertiary schooling completed between ages 30 and 39 in 1950 and the change in the log of population between 1930 and 1940 as covariates. Robust standard errors are in brackets, and ∗∗∗ , ∗∗ , and ∗ indicate significance at the 1-, 5-, and 10% levels, respectively.

Fig. 4. Change in log GDP per capita and change in predicted mortality, 1940-1980.

4. Conclusion This paper developed a growth theory in which the replacement of physical capital accumulation by human capital accumulation is endogenous, and mortality changes affect the replacement process. We focus on the difference between human and physical capital as a device of intrafamily transfer, presenting a novel channel through which the Ben-Porath effect operates. A testable prediction drawn from the theory is the heterogeneous effects of mortality on per-capita income among countries: the higher a country’s education level, the more likely it is that a decrease in mortality will increase income per capita. We applied an FMM approach to the causal estimation of Acemoglu and Johnson (2007), and confirmed that the prediction is supported by the data. Although our analysis is mainly descriptive, our findings have relevant policy implications. Simply introducing policies to improve health in poorer regions, where the education system is underdeveloped, might decrease per-capita income. Policies that promote education and improve health are needed to enable economies stuck in poverty to reach a growth path. The theoretical part of this study assumed mortality as an exogenous parameter, and analyzed the effect of exogenous changes in mortality. The empirical part of this study used an event where mortality changed exogenously (the international epidemiological transition) to test our theoretical predictions. Whether exogenous mortality has high validity depends on

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Table A.1 Estimation results for age population ratio. OLS Intervals of ages

20 years

Age ratio

35–54/15–54 [1]

40–59/20–59 [2]

30–44/15–44 [3]

35–49/20–49

40–54/25–54

45–59/30–59

[4]

[5]

[6]

−0.036∗∗ [0.015] −0.054∗∗∗ [0.009]

−0.016 [0.015] −0.026∗∗∗ [0.009]

−0.006 [0.014] −0.033∗∗∗ [0.008]

−0.038∗∗∗ [0.013] −0.055∗∗∗ [0.008]

−0.032∗∗ [0.014] −0.035∗∗∗ [0.009]

−0.002 [0.013] 0.004 [0.008]

47

47

47

47

47

47

Predicted mortality change Constant Number of countries

15 years

OLS. All regressions are long-difference specifications with two observations per country: for 1950 and 1980 in the dependent variables, and for 1940 and 1980 in the independent variable. The dependent variables for the age interval of 20 years are the age population ratio of 35–54 to 15–54 (column [1]), and the ratio of 40–59 to 20–59 (column [2]). The dependent variables for the age interval of 15 years are the age population ratio of 30–44 to 15–44 (column [3]), 35–49 to 20–49 (column [4]), 40–54 to 25–54 (column [5]) and 45–59 to 30–59 (column [6]). The independent variable is predicted mortality. Robust standard errors are shown in brackets, and ∗∗∗ , ∗∗ , and ∗ indicate significance at the 1-, 5-, and 10% levels, respectively.

the situation. A decrease in mortality by new drug development is exogenous, especially for developing countries, whereas a decrease in mortality via improved nutrition and sanitation is endogenous for many countries to some extent. Since human capital accumulation seems to play a key role in life expectancy improvements, endogenizing mortality in our framework, in which the replacement of physical capital accumulation by human capital accumulation is endogenous, would be an interesting direction for future research. It may help to consider how human capital and life expectancy interact with each other. Acknowledgments We thank Zheng Fang, Yu Liu, Yoichi Matsubayashi, Tamotsu Nakamura, an anonymous referee, the editor, and seminar and conference participants at Kobe University, Kwansei Gakuin University, Kyoto University, Nanyang Technological University, Sophia University, Ehime University, and the Japanese Economic Association Autumn Meeting 2015 for useful comments. We also thank David Lagakos for providing data. Yasui is grateful for financial support from JSPS KAKENHI Grant Number 15K17022 and 17H02516. Appendix A The empirical part of the paper (Section 3) focuses on the relationship between mortality change, per-capita income change, and initial education level. Although these elements are surely of central interest to our analysis, there are other elements crucially relevant to the proposed mechanism. In particular, changes in the age composition of the workforce and in the education level play key roles (see the description below Proposition 1). This appendix explores whether movements in the age composition of the workforce and in the education level after the international epidemiological transition were consistent with the predictions of our model. Age composition It follows from our model that a decrease in mortality increases the ratio of the adult workforce to the young workforce. To check whether this relationship holds in our sample, we regress the change in the proportion of the older working-age population on the change in predicted mortality. The estimation equation is

zi = κ + λ mi + ωi , where zi and mi are the change in the proportion of the older working-age population of country i between 1950 and 1980 and the change in the predicted mortality of country i between 1940 and 1980, respectively. We use the data of Barro and Lee (2013) for the population size by age. Table A.1 shows the estimation results. In order to check robustness, we use six types of measures, which differ in terms of the age interval, as proxies for the proportion of the older working-age population. A negative coefficient λ implies that a decrease in mortality increases the proportion of the older working-age population. Irrespective of the choice of age interval, the estimated coefficient is negative. Education It follows from our model that a decrease in mortality increases education only in the regime with positive education. To check whether this relationship holds in our sample, we split the sample into two groups (low and high initial education), and regress the change in log education on the change in predicted mortality for each group. The estimation equation is

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119

Table A.2 Estimation results for education. OLS Years of tertiary

Tertiary complete

30–39

Regime

Low [1]

High [2]

Low [3]

High [4]

Low [5]

High [6]

Low [7]

0.103 [0.402] 1.846∗∗∗ [0.273] 29

−0.809 [0.490] 1.025∗∗∗ [0.201]

0.135 [0.411] 1.774∗∗∗ [0.234]

−0.818∗ [0.392] 0.814∗∗∗ [0.172]

−0.703 [0.481] 1.051∗∗∗ [0.199]

−0.558 [0.426] −1.209∗∗∗ [0.293]

18

32

15

0.283 [0.381] 1.971∗∗∗ [0.258] 29

18

28

Predicted mortality change Constant Number of countries

30–49

30–39

No schooling

Age group

30–39 High

[8] 2.448∗∗ [0.916] 0.301 [0.442] 19

OLS. All regressions are long-difference specifications with two observations per country: for 1950 and 1980 in the dependent variables, and for 1940 and 1980 in the independent variable. The dependent variables are the log of years of tertiary schooling between ages 30 and 39 (columns [1] and [2]) and between ages 30 and 49 (columns [3] and [4]), tertiary schooling completed between ages 30 and 39 (columns [5] and [6]), and no schooling between ages 30 and 39 (columns [7] and [8]). The independent variable is predicted mortality. The High group indicates that the countries have an estimated probability of being in the “High” regime of more than 50% based on the corresponding estimations in Table 2, and the Low group consists of all other countries. Robust standard errors are shown in brackets, and ∗∗∗ , ∗∗ , and ∗ indicate significance at the 1-, 5-, and 10% levels, respectively.

j

j

j

ln xi = η j + χ j mi + ξi ,

j = Low, High,

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